How can I use Animated Strip Time in the NLA Editor?
Came across the same issue trying to use it. Whenever I made a keyframe it would resort back to 0 and wouldn't animate. 

I contacted the developer and it turns out this was a bug. It has now been fixed and it seems to be working fine on the latest daily build, which you can download from here:

https://builder.blender.org/download/


  UPDATE: Currently with the latest release (2.7a), you can only get it
  to work using the Graph Editor.